How to talk to someone who suffers from depression

I met a girl who lives in another state. I started to suspect that she suffers from depression. I know that she gets little to no sleep and at random hours. I have never met her in person. My sole communication if FB and Snapchat. She has not been open to talking on the phone or meeting in person, even though I would go to her. At first she was open, friendly, talkative, and flirtatious. She has said all along, she wants to be friends before anything else. Everything I said, she said that she really liked. Eventually, that went away. Particuarly, when I said I wanted to pursue something. She continues to flirt with other guys. She has told me mutliple times that she wants to be friends. However, she seems more distant and her responses shorter. She said, several times, she reads everything that I send, but she does not always want to talk about it. A few times, she opened up to me. I do not know if that is a positive sign. A week ago, I sent her a fliratious comment that we had shared several times, earlier. This time, she responded by telling me other guys hurt her and left her. She talks to me less and less, while other people more. She still likes my comments, or so she says. A few days ago, she was very flirtatious again. The next day, she had a very muted attitude toward it, as if she did not want that. She seems to hide her "excessivley flirtatious" side to me, while showing it to others. She puts off responding to me, for hours, where she never used to do that. A couple of times, I made jokes. She responded as if she was angry. I appologized and she replied that she was never mad. Just last night, she said she new that I would never intentionally upset her. This morning, she again said she reads everything, but she does not always respond because she is defensive. It's as if she is saying she is interested, but too scared. We talked about having a meaningful friendship. I sent her a supportive message that she really liked - or claimed to. This afternoon, she seems to be ignoring me, in favor of talking to others. Tomorrow, she may be very different.

I know that none of this means that she is depressed. She may simply tell me one thing and mean something else. I don't want to hurt her. I don't want to manipulate her. I truly care about her. I just don't know how to talk to her in a meaningful way. If she is pushing me away, tonight, how do I talk to her? When do I? When her responses are minimal, how can I really talk to her? Do I just rely on her reading what I say and hope to break through? After she told me about people leaving her, I shared one of my own secrets that I have never told anyone. I wanted it to be an investment in her. I have had my own past experiences with feeling depressed and empty - though not to the extent that she may feel. Like my previous experience, I thought of sharing that with her, but I don't know if it will help. Not in a way that accuses her, just sharing more of my own secrets. What should I do?